Risk quantification management diagnosis and hedgin

Risk Quantification Management, Diagnosis and Hedging Laurent Condamin Jean-Paul Louisot Patrick Na¨ım Risk Quantification For other titles in the Wiley Finance Series please see www.wiley.com/finance The authors would like to thank Bruno Bajard, David Breden, Gilles Deleuze and Philippe Garnier for their contributions to chapters 3, and Risk Quantification Management, Diagnosis and Hedging Laurent Condamin Jean-Paul Louisot Patrick Na¨ım Copyright C 2006 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on www.wiley.com All Rights Reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.co.uk, or faxed to (+44) 1243 770620 Designations used by companies to distinguish their products are often claimed as trademarks All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners The Publisher is not associated with any product or vendor mentioned in this book This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold on the understanding that the Publisher is not engaged in rendering professional services If professional advice or other expert assistance is required, the services of a competent professional should be sought Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 6045 Freemont Blvd, Mississauga, ONT, L5R 4J3, Canada Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books Library of Congress Cataloging-in-Publication Data Condamin, Laurent Risk quantification : management, diagnosis & hedging / Laurent Condamin, Jean-Paul Louisot, and Patrick Na¨ım p cm.—(Wiley series in financial engineering) Includes bibliographical references and index ISBN-13: 978-0-470-01907-8 (HB: alk paper) ISBN-10: 0-470-01907-7 (HB : alk paper) Risk management—Mathematical models I Louisot, Jean-Paul II Na¨ım, Patrick III Title HD61.C65 2007 658.15 5—dc22 2006033489 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 13 978-0-470-01907-8 (HB) ISBN 10 0-470-01907-7 (HB) Typeset in 10/12pt Times by TechBooks, New Delhi, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production Contents Foreword Introduction Foundations Risk management: principles and practice Definitions Systematic and unsystematic risk Insurable risks Exposure Management Risk management Risk management objectives Organizational objectives Other significant objectives Risk management decision process Step 1–Diagnosis of exposures Step 2–Risk treatment Step 3–Audit and corrective actions State of the art and the trends in risk management Risk profile, risk map or risk matrix Frequency × Severity Risk financing and strategic financing From risk management to strategic risk management From managing physical assets to managing reputation From risk manager to chief risk officer Why is risk quantification needed? Risk quantification – a knowledge-based approach Introduction Causal structure of risk Building a quantitative causal model of risk Exposure, frequency, and probability Exposure, occurrence, and impact drivers xi xiii 1 4 7 8 10 11 11 16 19 20 20 20 23 23 25 26 27 28 28 28 31 33 34 vi Contents Controlling exposure, occurrence, and impact Controllable, predictable, observable, and hidden drivers Cost of decisions Risk financing Risk management programme as an influence diagram Modelling an individual risk or the risk management programme Summary Tool Box Probability basics Introduction to probability theory Conditional probabilities Independence Bayes’ theorem Random variables Moments of a random variable Continuous random variables Main probability distributions Introduction–the binomial distribution Overview of usual distributions Fundamental theorems of probability theory Empirical estimation Estimating probabilities from data Fitting a distribution from data Expert estimation From data to knowledge Estimating probabilities from expert knowledge Estimating a distribution from expert knowledge Identifying the causal structure of a domain Conclusion Bayesian networks and influence diagrams Introduction to the case Introduction to Bayesian networks Nodes and variables Probabilities Dependencies Inference Learning Extension to influence diagrams Introduction to Monte Carlo simulation Introduction Introductory example: structured funds Risk management example – hedging weather risk Description Collecting information Model 35 35 36 37 38 39 41 43 43 43 45 49 50 54 57 58 62 62 64 67 68 68 69 71 71 73 74 74 75 76 77 78 79 79 81 83 85 87 90 90 90 96 96 98 99 Contents Manual scenario Monte Carlo simulation Summary Risk management example 2– potential earthquake in cement industry Analysis Model Monte Carlo simulation Conclusion A bit of theory Introduction Definition Estimation according to Monte Carlo simulation Random variable generation Variance reduction Software tools Quantitative Risk Assessment: A Knowledge Modelling Process Introduction Increasing awareness of exposures and stakes Objectives of risk assessment Issues in risk quantification Risk quantification: a knowledge management process The basel II framework for operational risk Introduction The three pillars Operational risk The basic indicator approach The sound practices paper The standardized approach The alternative standardized approach The advanced measurement approaches (AMA) Risk mitigation Partial use Conclusion Identification and mapping of loss exposures Quantification of loss exposures The candidate scenarios for quantitative risk assessment The exposure, occurrence, impact (XOI) model Modelling and conditioning exposure at peril Summary Modelling and conditioning occurrence Consistency of exposure and occurrence Evaluating the probability of occurrence Conditioning the probability of occurrence Summary Modelling and conditioning impact vii 101 101 104 104 104 106 107 109 109 109 110 111 112 113 117 119 119 119 120 121 122 122 123 123 124 124 125 125 127 127 130 130 131 131 134 134 135 135 136 137 137 140 143 144 145 Risk Financing 257 Individual loss STO SPO SPL EXL STL SPC STC Cumulative loss Number of occurrences Figure 5.18 3D representation of an elementary cover the cumulated covered euros before the selected euro, and finally let O denote the number of losses occurrences, starting from the beginning of the cover period Then the considered euro is covered if and only if the three conditions below hold simultaneously: ST L + E X L ≤ L ≤ ST L + S P L ST C ≤ C ≤ ST C + S PC ST O ≤ O ≤ ST O + S P O In this case, the specified fraction of the considered euro (FOL) is covered Otherwise this particular euro is not covered In this visual representation, building an efficient financing tool can be interpreted as positioning some elementary blocks in an appropriate way Usual financing tools revisited Let us discuss how classical financing tools may be described using these building blocks r r r r r r Retention (self-insurance and informal retention) First line insurance Excess insurance Retro-tariff insurance Captive insurer ART (cat bonds) 258 Risk Quantification Table 5.18 Informal retention cover features Parameter Value Comment STL SPL EXL FOL STC SPC STO SPO Infinity — — — — — — — Every loss is retained Nothing is transferred Informal retention Informal retention is the “minimal” method to finance risks Losses are paid when they occur This kind of programme can be described by the instance of the model shown in Table 5.18 Self-insurance Self-insurance is very similar to informal retention The main difference stems from the fact that self-insurance is a formal process set by the organization to handle losses Therefore, there is a difference for the cost features but not the cover features First line insurance First line insurance covers an organization between the first euro and a maximum amount An excess can be applied on each occurrence Table 5.19 describes an example of a product liability insurance, which covers losses for a maximum amount of €1m with a stop-loss of €10m, with an excess per occurrence of €100 000 Excess insurance Excess insurance covers an organization for losses that could occur, in excess of a given amount Generally speaking, they are used on top of a first line insurance Table 5.20 represents an excess insurance built on top of the previous one to cover liability losses for an amount of €5m in excess of €1m No excess per occurrence is defined and a stop-loss of €50m is set Table 5.19 First line insurance cover features Parameter Value STL SPL EXL FOL STC SPC 100 % — €10m STO SPO — — €1m €100k Comment The first ero is covered Losses between €0 and €1m are covered €100 000 are retained for each event If cumulative loss exceeds €10m, losses are not covered any more Risk Financing 259 Table 5.20 Excess insurance cover features Parameter Value STL SPL EXL FOL STC SPC €1m €5m 0€ 100 % — €50m STO SPO — — Comment Losses under €1m are retained Losses between €1m and €6m (1 + 5) are covered If cumulative loss exceeds €50m, losses are not covered any more Retro-tariff insurance Retro-tariff insurance aims to cover both individual losses and cumulative losses in excess The organization retains losses that are under a limit per event and as long as its cumulative retained losses remains under a cumulative limit The organization has to pay a fixed prime for transferred losses (above the limit per event) and a loss adjusted prime for losses under the limit This is why losses under the limit can be considered as retained Retro-tariff insurance cannot be represented with a single block since its space representation is not a rectangle any more but the union of two rectangles: a euro is covered if it lies between a minimal and a maximal individual loss or if it lies above a minimal cumulative loss In Tables 5.21 and 5.22, we present a retro-tariff insurance with a limit per event of €100 000, an amount covered of €1m, and a limit on cumulative losses of €5m The insurance is obtained by combining through ensemble reunion an excess insurance block and a specific block which starts covering losses when a cumulative loss of €5m is reached, Figure 5.19 Captive insurer From the organization’s point of view, a captive insurer can be modelled as any of the insurance tools Therefore we will change our perspective and study a financial tool used by captive insurers or classical insurers in order to cover their own losses: reinsurance We will focus on quotashare reinsurance Table 5.21 Retro-tariff insurance – block Parameter Value STL SPL EXL FOL STC SPC STO SPO €100k €1m €0 100 % — — — — Comment Losses under €100 000 are retained Losses between €100 000 and €1.1m(€100k + €1m) are covered 260 Risk Quantification Table 5.22 Retro-tariff insurance – block Parameter Value Comment STL SPL EXL FOL STC SPC STO SPO — — — 100 % €5m — — — As soon as cumulative loss exceeds €5m, losses are covered Up to now, we considered that either a euro was covered or it was retained With quota-share reinsurance, this rule does not hold any longer: a euro may be only partly covered When an insurer transfers his own risks to a reinsurer within the framework of a quota-share programme, the fraction of transferred losses is equal to the fraction of the premium paid to the reinsurer For example, if the reinsurer received 75 % of the risk prime paid by the insurer client, he will also have to pay 75 % of the losses: on a €1 loss, the insurer will retain 25 cents and transfer 75 cents to the reinsurer Table 5.23 represents a reinsurance quota-share programme which covers the insurer for 75 % of losses that could incur from the excess insurance tool described above The cover definition includes all losses that are transferred by the organization to the insurer Losses are being considered from the insurer’s point of view Alternative risk transfer Alternative risk transfer (ART) tools might be as complex as desired according to the organization objectives A multi-stage process based on captive, reinsurance, Loss €1.1m €100k €5m Cumulative loss Figure 5.19 Retro-tariff insurance as a combination of two building blocks The grey area is covered Risk Financing 261 Table 5.23 Quota share reinsurance Parameter Value Comment STL SPL €0m EXL FOL STC SPC STO SPO €0 75 % — — — — From the insurer’s point of view, a loss is covered as soon as it occurs Limit is not defined here But we know from the cover definition that losses should not exceed €6m — 75 % of the loss is covered and financial products might be necessary to meet coverage requirements Besides the classical insurance tools, ART relies on financial markets to transfer some special risks (cat nat, marketbased risks, etc.) Most of the used financial tools are cat bonds and insurance derivatives Whatever the underlying technical difficulties may be to implement these tools, they transfer the risks from the organization to the financial market instead of an insurer Cat bonds, swaps, and insurance options can be modelled as standard insurance Combining a risk model and a financing model The model discussed above for an elementary financing block can be used to represent a large set of classical financing solutions Representing more complex financing solutions involves combining several elementary blocks in order to cover the possible losses in the most appropriate way A financing solution may be considered as a set of elementary blocks which aims at covering the potential losses without forgetting some “holes” As a consequence, blocks will generally depend on each other For example, if we want to build a two-layered insurance with an excess insurance on top of a first line insurance, the excess of the excess insurance should be equal to the amount covered by the first line insurance, Figure 5.20 To decide whether a euro is covered by any of the elementary blocks involved in the financing tool being studied, we have to scan each of the elementary blocks in a given order and stop whenever the considered euro satisfies the cover conditions A financing tool can be thus considered as an ordered set of elementary covers If we return to the above example, we have two elementary covers numbered for the first line and for the excess line SPL1 = €100k STL1 = €0 SPL2 = €400k STL2 = €100k = SPL1 Figure 5.20 Amount covered by the first line is the excess of the excess insurance €500k Loss 262 Risk Quantification Financing tool Covered losses Losses Risk model Exposure 2 cover no.1 € cover no.2 € cover no.3 € cover no.p € Occurrence Severity Cost of risk Retained losses € Figure 5.21 A general Monte Carlo simulation framework for risk financing If we assume that an event meets the cover definition, the process of deciding whether a euro is covered must be done as follows: Check whether this euro is between and 100 000: If the answer is “yes”, then stop: this euro is covered by the first line insurance Otherwise, proceed to the next block Check whether this euro is between 100 000 and 500 000: If the answer is “yes”, then stop: this euro is covered by the excess insurance Otherwise, proceed to the next block This euro is retained by the organization In real life, some overlaps may exist between different covers In order to simplify our discussion, we will assume that elementary covers not overlap For a given financing tool, let us assume that this tool can be described as a combination of interdependent elementary building blocks Then it is possible for any euro of a given loss to decide whether this euro is covered, and it is possible to identify which building block was activated for this coverage This method for dispatching loss euros must be implemented as part of the loss model, in order to be able to compute (1) the distribution of losses covered by each elementary financing block, and (2) the distribution of the losses retained by the organization The cost features of the risk financing solution should be integrated in the model as well, if one wishes to calculate the distribution of the total cost of risks Figure 5.21 describes this global process for risk financing quantification On the left, the organization’s risk model quantifies the exposure at peril, the loss occurrence probability, and the loss severity This model is used to sample one year of losses (or any other period of time) Each loss is characterized by the object that has been hit, the sequence number of the occurrence from the beginning of the considered period of time, and the loss severity Risk Financing 263 For each loss, its amount will be sent through the “dispatching rules” of the financing solution in place Each elementary cover will keep track of the cumulated covered losses and calculate the cost of risks according to its cost features When cost features are not defined at the level of an elementary cover, cost is calculated at the level of its parent cover (the cover it is part of) By applying this process several times, i.e through Monte Carlo simulation, we sample several years of risks of the considered organization This allows us to calculate the distributions of cumulated losses, covered losses, retained losses, and risk costs The inputs of this process are: r r Exposure, occurrence and severity distributions for each risk being considered Cover features and cost features for the elementary blocks of the chosen financing solution The outputs of this process are: r r r Distribution of cumulated retained losses Distribution of cumulated transferred losses dispatched over each cover Distribution of cost of risks Such a process can be summarized by an influence diagram (see Figure 5.22) where: r r r Decision nodes are cover features and cost features for the financing tools Input distribution nodes are the exposure, the occurrence, and the loss impact of the considered risks (risk model) Output distribution nodes are cumulated retained losses, cumulated transferred losses, and cost of risks This influence diagram represents a particular implementation of the general influence diagram introduced in Figure 5.21 Risk model Cover features STO SPO STL SPL FOL EXL STC SPC Cost features Occurrence Exposure STO SPO STL SPL FOL EXL STC SPC Severity Retained risks losses Transferred risks losses Cost of risk Figure 5.22 The influence diagram for risk financing This diagram is based on exposure, occurrence, severity risk model(s) and on the decomposition of the financing solution into elementary covers The cover features have to satisfy some constraints to account for dependency among elementary covers 264 Risk Quantification If we modify the cover features or the cost features of the financing solution, all the output distributions will be impacted We can hence compare several financing solutions by playing with decision nodes The risk model is based on exposure, occurrence, severity framework which was previously introduced in Chapter 3, but it could be replaced by any available risk model developed by the organization provided that this model works at the level of individual losses and not only at the level of aggregate losses This constraint on risk model stems from the fact that financing tools generally specify limits on individual event losses, as was shown before CONCLUSION In the two previous chapters, we have studied why risk quantification is useful for risk diagnostic and risk control These two steps of the risk management process involve an accurate knowledge of the risks an organization has to face and of the levers it could use to control risks For these steps, although extremely useful, quantification is not always mandatory: under certain circumstances, an organization can still rely on qualitative assessment to identify and control its risks For risk financing, qualitative assessment is definitely not adequate to deal with calculating premiums, losses, volatility, etc An accurate quantification of risks is necessary for a rational risk financing Several reasons require the risk manager to address the quantification of its risks At first, an organization should know if its financing programme is well suited for the perils it has to face Financing programme features must be linked to the distribution of potential losses that have to be covered The questions are: “Is the organization protected against severe losses?” and “Are retained risks mastered so as to reduce their volatility and their maximal level?” Answers to these questions cannot be based on qualitative assessment of risks Quantitative risk models are the basic tools to run an efficient analysis of this issue Second, when an organization has to negotiate with insurers or insurance brokers, it has to be aware of the risks it wants to transfer and more precisely of the distribution of the potential losses that could be transferred This quantitative assessment of risks should allow the organization to evaluate the theoretical insurance primes On their side, insurers rely on internal quantitative models generally based on actuary studies or on expert knowledge (especially for disaster scenarios) However, the organization generally has a more accurate knowledge of its own risks, at least for exceptional events which would not be represented in insurance companies’ databases The best situation is found when both insurers and organizations share their knowledge to build an accurate model of risks Third, the optimization of an existing financing programme or the design and selection of a new one requires building quantitative models In the first case, the quantitative model will help to identify the key financing features required to improve the organization’s coverage In the second case, plugging the different financing alternatives with the risk model will give the organization a clear view of the risks it would have to retain and transfer As shown in this chapter, modelling the risks is not sufficient if we want to address the objectives listed above We also have to model the financing programme We have proposed a general framework where any financing programme can be considered as a set of elementary financing blocks and we have proposed a model for this elementary financing block This model is suited to a range of classical financing tools – self-insurance and informal retention, first line insurance, excess insurance, retro-tariff insurance, captive insurer, cat bonds – but it Risk Financing 265 might be insufficient or should be adapted to take into account some complex financing set-up But the more complex the financing programme seems to be, the more the organization should try to catch this complexity inside a model But even if an organization did its best and built an accurate model of risks and financing tools, even if it is able to evaluate the theoretical premium it should pay, the market will decide the actual price the organization should pay to transfer its risks This market may be unbalanced for some special risks When the insurance offer is unavailable, actual premiums could be very different from theoretical primes calculated by models Does this argument invalidate the need for accurate quantification of risks? No for at least two reasons: first, even if the final cost of transfer depends on the insurance market, the organization should be aware of that fact and should know the price it has to pay because of the insufficient liquidity on the market Second, the liquidity of the insurance markets is likely to increase as they get connected to the capital markets The efficiency of these markets lets us expect that the price to be paid for risk transfer will tend to be the “right” one Index accident, 29 advanced measurement approaches (AMA), for calculating operational risks, 127–130 airline terrorist risk model, 39 AIRMIC, 28 ALARM, 28 Bachelier, Louis, 75–76 banking risks, 23 Barings Bank, 73 Basel II agreement, 120, see also Basel II framework, for operational risk Basel II Consultative paper, 123 Basel II framework, for operational risk, see also loss exposures, quantification of advanced measurement approaches for calculating operational risks, 127–130 Basel II reporting matrix, 132 definition of, 124 essentials for branch operations, 132 indicator approach for calculating operational risks, 124 management principles of operational risks, 125 pillars of, 123–124 risk mitigation, 130 standardized approach for calculating operational risks, 125–127 Basel II regulations, 123 Basel I regulations, 123 Bayes, Thomas, 119 Bayesian networks, 29, 70, 134, 149, 243 for analysis of vaccination policy, 87–90 calculation of road transport fleet risk using extension of influence diagrams, 87–90 inference, 83–85 introduction to Bayesian network, 78–83 introduction to case, 77 knowledge aquisition in, 85–86 dependencies, 81–83 nodes and variables in, 79 probabilities, 79–81 Bayes’ theorem, 50–54, 57 belief revision process, 50–51 binomial distribution, 62–63 bonus, 165 British Airways, 26 British Petroleum, 26 capital adequacy equation, 123 capital charges, 126 cargo road accident model, 39 catastrophic events, 1, 170 central limit theorem, 68, 188 chief risk officer, 26–27 cindynic potential, 172 cindynics, basic concepts, 170–172 axioms in, 174–175 dysfunctions, 172–174 general principles, 174 perspectives, 174–176 cindynic situation, 170 claims management, 21 Cluedo game, 51–54 Committee for Banking Supervision, 128 conditional probability, see probability basics contractual risk transfer, 164–165 credit cards, 32 cumulative distribution function (CDF), 59, 61 decision nodes, 30 diversifiable risk, duplication, 167 economic efficiency, Efficient Market Hypothesis (EMH), 76 268 Index enterprise social responsibility, environmental risks, 119 European wheel roulette game, 43, 55 exposure, definition of, 7, 32 exposure, measurement of, 135 external auditors, 128 Exxon Valdez, 26 family systematic therapy, 173 “fat finger” error, 135 “fat finger” scenario, 150–157 “fault tree analysis” technique, 141 Fayol, Henri, 27 FERMA, 28 Firestone, 26 Fisher – Tippett distribution, 66 foreign exchange risk, 24 foreign war, see military risk frequency risks, 166 frequency × severity matrix, 20–22 Gaussian distribution, 63 GESTRISK, global attack rate, 187 globalization, 25 gross income, 124, 126 Gumbel distribution, 66 hazardous situation, 170 hazards, health risk, 24 Heisenberg’s uncertainty principle, 29 histogram distribution, 66 impact, measurement of, 135 equations and variables for different scenarios, 146 influence diagram, 31 influenza pandemic risk model Bayesian network, 180 exposure, 177 impact, 178–179 occurence, 177 insurable risks, 4–7 insurance premium, 21 intangible assets, interest rate risks, 24 internal fraud” risk, 136, 138 intrinsic cost, 162 investment risk, 24 IRM, 28 ISO 73 document, Katrina, 119 knowledge management, 120 KPMG, 26 liquidity risk, 23 Lisbon earthquake, 169 loss control category of drivers in, 163 loss prevention contractual risk transfer, 164–165 elimination of exposure, 164 reducing frequency of occurance, 166 risk avoidance or suppression, 164 loss reduction active reduction, 167–168 duplication, 167 passive reduction, 166 post-event redeployment planning, 168–169 separation, 166–167 Loss Distribution Approach (LDA), 121, 134, 157 loss exposures, quantification of, see also Basel II framework, for operational risk candidate scenarios for quantitative risk assessment, 134 conditioning of exposure, 137 measurements for exposure to different types of risk, 136 modelling and conditioning exposure at peril, 135–136 modelling and conditioning impact distribution variables involved, 146–147 impact drivers, 147–148 impact equation, 145 modelling and conditioning occurrence conditioning the probability of occurrence, 143–144 consistency of exposure and occurrence, 137–140 evaluating the probability of occurrence, 140–143 modelling the global distribution of losses, 158 quantifying scenarios, 148–150 example of, 150–157 variable quantification method, 147 XOI model, 135, 149 machine complexity, 29 management, definition of, Maquet, Yves, 13 Meltzer’s original paper, 181, 185 military risk, 24 mixed risks, Monte Carlo simulation, 134, 149 for analysis of potential earthquake in cement industry computation model, development of, 106–107 context, 104–106 Monte Carlo simulation of net present value, 107–109 Index application of control variable technique in, 113–114 background of, 109–110 definition of, 110–111 estimation according to, 111–112 hedging of weather risk computational model, development of, 99–100 data collection, 98–99 introduction to case, 96–97 manual analysis of scenario using model, 101 Monte Carlo simulation of potential losses, 101–104 random variable generation in, 112–113 software tools used in, 117 for structured funds, 90–92 application of sampling random numbers, 92–94 building structured fund simulation, 94–96 use of antithetic variable sampling in, 114 use of Latin hypercube sampling, 115–117 use of stratified sampling, 115 variance reduction in, 113 natural disasters, Neumann, John von, 109 nondiversifiable risk, none strategy, 183 object of risk categories in, concept of, occurrence, measurement of, 135 empirical evaluation, 140 subjective evaluation, 141 theoretical evaluation, 140 organization definition of, resources of, perceptual salience, theory of, 74 peril, 5, 32–33, 140 classification of, 5–6 financial loss by, vs hazards, Perrier, 26 physical assets, Pillar One rules, 124 Poisson distribution, 65 probability basics axioms in, 43–45 Bayes’ theorem, 50–54 conditional probabilities, 45–49, 56 empirical estimation of probabilities, 68–71 expert estimation of probabilities, 71–75 269 independence, 49–50 maximum likelihood estimation, of probabilities, 69 probability density function, 61 probability distributions, 62–67 random variables, 54–57 moments of, 57–61 theorems in, 43–45, 67–68 unconditional probability, 56 procurement management, project risk, 24 PTAll strategy, 183 PTHiRisk strategy, 183, 187 pure risk, quality management, quantitative risk assessment, see also Basel II framework, for operational risk features of risk assessment, 119–120 issues in risk quantification, 121 objectives of risk assessment, 120–121 random variables, 54–57 correlation of, 58 covariance of, 58 expected value of, 57–58 moments of, 57–62 standard deviation of, 58 2000 readiness crisis management team, reputation, concept of, 25–26 residual risk, 165 resilience planning process, 168 risk centres, 11, 131 method, 13–14 risk control, quantitative modelling of economic impact of pandemic influenza context, 176 influenza pandemic risk model, 177–181 risk analysis, 188–189 risk control strategies, 181–187 enterprise-wide risk management application to the risk management of an industrial plant, 203–210 context and objectives, 195 representation using Bayesian networks, 196–201 risk analysis and complex systems, 195–196 usage of the model for loss control, 201–202 “fat fingers” operational risk model analyses of potential severe losses, 189 analysing the cumulated impact of loss control actions, 190–191 identifying the loss control actions, 189–190 risk analysis, 192–193 270 Index risk financing, see also risk financing, with quantitative models alternative risk transfer (ART) tools, 260–261 building blocks in, 254–257 captive insurer, 259–260 combination of risk model and financing model in, 261–264 excess insurance, 258 financing tools in, 257 first line insurance, 258 informal retention, 258 instruments capital markets products for risk financing, 225–230 choice of retention levels, 222–223 financial reinsurance and finite risks, 223–225 hybrid techniques, 220–222 retention techniques, 214–219 risk financing and risk quantifying, 230 transfer techniques, 219–220 retro-tariff insurance, 259 self-insurance, 258 risk financing, with quantitative models case example of property insurance programme calculation of perils, 243–244 computation of losses, 250 context and objectives, 243 financial programme in, 248–249 quantification of impacts, 245–248 risk analysis, 250–252 case example of satellite launcher context and objectives, 231 development of risk model, 231 financing programme, 231–232 implementation of Monte Carlo simulation, 235–243 probabilistic analysis of failures, 232–233 set up and operating conditions, quantitative analysis of, 233–235 risk management, see also Basel II framework, for operational risk Australian standards, 28 British standards, 28 causal graph for, 38–39 circle of, 18 classification of perils, concepts in, 3–8 decision process in audit and corrective actions, 19–20 diagnosis of exposures, 11–16 risk treatment, 16–19 financial risks, 23–24 identification tools for expert analyses, 13 financial and accounting records, 12 historical data and scenario analysis, 12–13 marketing, purchasing and other documents, 12 production and flow charts, 12 site inspection, 13 standards questionnaires, 12 information system for, of insurance company, loss control techniques, 17 marketing techniques in, model for, 39–40 nonfinancial risk, 24 objectives economic efficiency, environmental issues, 8–9 ethics and good citizenship, functional objectives, at operational level, 9–10 at organizational level, other objectives, 10 permanent objective of manager, 14 risk financing techniques, 17 risk quantification changes in frequency due to exposure and probability, 33–34 cost of decisions, 36–37 drivers of risk exposure variables, 35–36 impact drivers in, 34–35 quantitative causal model of risk, 31–33 risk financing, 37 trends in physical asset management, 25–26 risk financing and strategic financing, 23 in risk management professional skills, 26–28 risk management vs strategic management, 23–25 risk matrix, 20–22 risk mapping, 22 risk mitigation, 130 risk premium, risk quantification, 122 changes in frequency due to exposure and probability, 33–34 cost of decisions, 36–37 drivers of risk exposure variables, 35–36 impact drivers in, 34–35 quantitative causal model of risk, 31–33 risk financing, 37, see also risk financing separation, 166 Shell, 26 social environment, 172 speculative risk, stakeholders, 165 stochastic process, 62 Index suppression, 164 systematic risk, tangible assets, 9/11 terrorist attacks, 119 transferee, 165 transferor, 165 triangular distribution, 67, 74 Truffle Fund, 90–96 Ulam, Stanislaw, 109 uncertain event, 48, 63 unsystematic risk, user experience, 29 US stock returns distribution, 60 utility graph, 162 utility nodes, 30 VAll strategy, 183, 185, 187 Venn diagrams, 44–45 VHiRisk strategy, 183 weak law, of large numbers, 67 weather conditions risk, 24 Weibull distribution, 64 World Health Organization, 170 XOI model, see loss exposures, quantification of Year 2000 bug, 1, 25 zero cover, 168 zero defects, zero inventories, 271 ... Introduction Foundations Risk management: principles and practice Definitions Systematic and unsystematic risk Insurable risks Exposure Management Risk management Risk management objectives Organizational... objectives Risk management decision process Step 1 Diagnosis of exposures Step 2 Risk treatment Step 3–Audit and corrective actions State of the art and the trends in risk management Risk profile, risk. . .Risk Quantification Management, Diagnosis and Hedging Laurent Condamin Jean-Paul Louisot Patrick Na¨ım Risk Quantification For other titles in the Wiley